On the Switch Markov Chain for Perfect Matchings
Copyright policy )On the Switch Markov Chain for Perfect Matchings
We study a simple Markov chain, the switch chain, on the set of all perfect matchings in a bipartite graph. This Markov chain was proposed by Diaconis, Graham and Holmes as a possible approach to a sampling problem arising in Statistics. We ask: for which hereditary classes of graphs is the Markov chain ergodic and for which is it rapidly mixing? We provide a precise answer to the ergodicity question and close bounds on the mixing question. We show for the first time that the mixing time of the switch chain is polynomial in the case of monotone graphs, a class that includes examples of interest in the statistical setting.
- University of Leeds United Kingdom
- Queen Mary University of London United Kingdom
- White Rose Consortium: University of Leeds; University of Sheffield; University of York United Kingdom
- School of Mathematical Sciences, Queen Mary University of London United Kingdom
- Queen Mary University of London
FOS: Computer and information sciences, bipartite graphs, hereditary graph classes, Counting problems, perfect matching, permanent, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO)
FOS: Computer and information sciences, bipartite graphs, hereditary graph classes, Counting problems, perfect matching, permanent, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO)
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